## 3D Printed Tippe Top

After setting up my newest toy, the Creality Ender 3 V2 3D Printer, I started with a few simple prints from the Thingiverse website. The first Physics-related object created is for a colleague – a tippe top. This interesting mushroom-shaped toy is spun with the round top facing down. If it is spun fast enough, it will eventually spin upright, in the opposite orientation to where it started spinning. In doing so, it’s centre of mass even shifted upwards.

The source of the STL file is: https://www.thingiverse.com/thing:536377

The following video gives an explanation for why this happens.

## Pendulum-Powered Car

This pendulum-powered car is constructed using Lego Technic parts. I used mainly Lego beams to create the chassis and an “A” frame from which the pendulum is suspended. The pendulum is made of Lego beams and some wheels.

When the pendulum swings, it experiences an acceleration towards its equilibrium position. By the principle of conservation of momentum, the car experiences a change in momentum in the opposite direction. Since the acceleration of the pendulum changes its direction every half a cycle of its oscillation, the car will only oscillate about its original position if the wheels of the car are free to turn throughout the oscillation.

A escapement mechanism which consists of a beam resting on a pair of 40-tooth gears attached to the front wheels prevent the wheels from rotating in the opposite direction. This means that the car will only be moving forward during the half of the pendulum’s oscillation when its displacement is at the front of its equilibrium position and pauses during the other half.

## Simple harmonic motion graphs including energy

I have added two more graphs into the interactive animation. However, the app has become a bit sluggish when changing the period or amplitude. It still works smoothly when viewing the animation.

Students ought to find it useful to look at all the graphs together instead of in silo. This way, they can better understand the relationships between the graphs.

As usual, here is the animated gif file.

## Simple Harmonic Motion Graphs

Here’s my attempt at animating 5 graphs for simple harmonic motion together in one page.

From left column:

$$v = \pm\omega\sqrt{x_o^2-x^2}$$

$$a = -\omega^2x$$

From right column:

$$s = x_o\sin(\omega t)$$

$$v = x_o\omega \cos(\omega t)$$

$$a = -x_o\omega^2 \sin(\omega t)$$

And here is the animated gif file for powerpoint users:

## Phase Difference

The first of two apps on Phase Difference allows for interaction to demonstrate the oscillation of two different particles along the same wave with a variable phase difference.

The second shows two waves also with a phase difference.

In both cases, the phase difference $\Delta\phi$ can be calculated with

$$\Delta\phi = \dfrac{\Delta x}{\lambda} \times 2\pi$$

where $\Delta x$ is the horizontal distance between the two particles or the horizontal distance between the two adjacent identical particles (one from each wave) and $\lambda$ is the wavelength of the waves.